Shalit was captured in a cross-border raid by Palestinian fighters in June 2006.
Olmert is in the final days of a three-year term marked by a 2006 Lebanon war that many Israelis see as a failure and a 22-day Gaza campaign that ended in January without achieving a complete halt to cross-border rocket fire.
The outgoing prime minister has refused to agree to an Egyptian-proposed ceasefire with Hamas and opening the territory's border crossings more fully until Shalit is freed.
Olmert is thought to be ready to release about 450 Palestinians in exchange for Shalit.
Israel has carried out lopsided exchanges in the past, trading large numbers of Arab prisoners for its captured soldiers or their remains.
Members of Olmert's outgoing administration have cautioned that Hamas may find the next Israeli government, currently being formed by Benjamin Netanyahu, the Likud leader, less willing to deal on prisoners.